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Simplifying 3x(x + -6) = 5x + 20 Reorder the terms: 3x(-6 + x) = 5x + 20 (-6 * 3x + x * 3x) = 5x + 20 (-18x + 3x2) = 5x + 20 Reorder the terms: -18x + 3x2 = 20 + 5x Solving -18x + 3x2 = 20 + 5x Solving for variable 'x'. Reorder the terms: -20 + -18x + -5x + 3x2 = 20 + 5x + -20 + -5x Combine like terms: -18x + -5x = -23x -20 + -23x + 3x2 = 20 + 5x + -20 + -5x Reorder the terms: -20 + -23x + 3x2 = 20 + -20 + 5x + -5x Combine like terms: 20 + -20 = 0 -20 + -23x + 3x2 = 0 + 5x + -5x -20 + -23x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -20 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -7.666666667x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -7.666666667x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + 6.666666667 -7.666666667x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -7.666666667x + x2 = 6.666666667 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 6.666666667 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 6.666666667 + 14.69444445 Combine like terms: 6.666666667 + 14.69444445 = 21.361111117 14.69444445 + -7.666666667x + x2 = 21.361111117 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 21.361111117 Calculate the square root of the right side: 4.621808209 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.621808209 and -4.621808209.Subproblem 1
x + -3.833333334 = 4.621808209 Simplifying x + -3.833333334 = 4.621808209 Reorder the terms: -3.833333334 + x = 4.621808209 Solving -3.833333334 + x = 4.621808209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.621808209 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.621808209 + 3.833333334 x = 4.621808209 + 3.833333334 Combine like terms: 4.621808209 + 3.833333334 = 8.455141543 x = 8.455141543 Simplifying x = 8.455141543Subproblem 2
x + -3.833333334 = -4.621808209 Simplifying x + -3.833333334 = -4.621808209 Reorder the terms: -3.833333334 + x = -4.621808209 Solving -3.833333334 + x = -4.621808209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.621808209 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.621808209 + 3.833333334 x = -4.621808209 + 3.833333334 Combine like terms: -4.621808209 + 3.833333334 = -0.788474875 x = -0.788474875 Simplifying x = -0.788474875Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.455141543, -0.788474875}
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